For those who know mathematicians and those who don't.

Pay deep respect to those promoters of civilization.

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There are two kinds of beauty.

One is a profound and moving equation.

First of all, you have a tired faint smile.

Euler stopped living, so he stopped calculating.

-de condorcet

In a topology class, Minkowski proudly declared to the students: "The most important reason why this theorem has not been proved is that only some third-rate mathematicians have spent time on it so far. Now I will prove it ... "So Minkowski began to pick up the chalk. This class is over, and the certificate has not been issued yet. In the next class, Minkowski continued to prove that several weeks had passed ... One cloudy morning, Minkowski walked into the classroom. It was like lightning across the sky, and the thunder was deafening. Minkowski said very seriously: "God was angered by my pride, and my proof was incomplete ..."

Hilbert once had a student who gave him a paper to prove Riemann's conjecture. Although there was an irreparable mistake, Hilbert was deeply attracted. The next year, the student died somehow, and Hilbert asked to give a speech at the funeral. That day, the wind and rain were rustling, and the students' families were full of grief. Hilbert began his speech, first pointing out that it is a pity that such a genius left us so early. Everyone felt the same way and cried more and more fiercely. Then Hilbert said that although this person's proof is wrong, if we follow this road, we should be able to prove Riemann's conjecture. Then, Hilbert continued to preach enthusiastically in the rain: "Actually, let's consider a univariate complex variable function …" Everyone fell down.

Proved to be an idol, mathematicians tortured themselves in front of this idol.

-Eddington

There was a man named Wolfskeil, who studied mathematics in college and was crazy about a beautiful girl. To his dismay, he was rejected countless times and felt helpless, so he set a date for suicide and decided to bid farewell to this world and never care about worldly affairs again when the midnight bell rang. Wolfsker is still working hard for the rest of his life, not math, but something commercial. On the last day, he wrote a will and wrote letters to all his friends and relatives. Because of his high efficiency, he finished everything before midnight. In the remaining hours, he ran to the library to look through his math books. Soon, I was attracted by a paper by Cuomo, which explained why Cauchy and other predecessors could not do Fermat's Last Theorem. That's a great paper for mathematicians who want to commit suicide to read at the last minute. Wolfskehl actually found a bug in Kummer, and he proved it until dawn. He was so arrogant that everything became a thing of the past ... In this way, he made a new will, and set a large part of his property as a reward, telling the first person who proved Fermat's last theorem that 654.38 million marks ... This is the origin of the Wolfskeil Prize.

On the wall at the bottom of the city hall in G? ttingen, it is bluntly engraved:

"There is no life outside G? ttingen."

1854, Riemann gave his epoch-making geometry lecture in order to get a lecturer's seat in G? ttingen (the center of mathematics and physics before World War II, a famous German university). Because many people who listened to this speech at that time were school administrators and didn't understand mathematics at all, Riemann only used a mathematical formula in his speech. Weber recalled that at the end of the speech, Gauss excitedly praised Riemann's idea with a rare expression. If you read Riemann's lecture, you will find that it is almost philosophy. Even so, only one person in the audience at that time could understand Riemann, and that was Gauss. However, it took the whole mathematics community nearly 65,438+000 years to perfect and digest Riemann's thought.

Some people say that Riemann's works are closer to philosophy than mathematics. Even at the beginning, many mathematicians in Europe thought that Riemann's works were family publications, which were closer to the views of physicists and had nothing to do with mathematicians. On one occasion, Helmholtz and Vesteras went on vacation together, and Vesteras took a doctoral thesis of Riemann with him, so that he could study this complex and magnificent work quietly in a beautiful environment. But Helm holz was puzzled. He thinks Riemann's article is clear enough. Why does Vesteras work so hard as a mathematician?

Let's start with d Hilbert.

David Hilbert did not graduate from the University of G? ttingen. In the 65438+1980s, Berlin University needed two students as opponents, and they kept asking you questions. One of Hilbert's opponents was Emil Wiechert, and later he was the most famous seismologist. At that time, there were very few university professors in Germany (maybe Prussia). There are only three mathematics professors in Berlin, and there are at most two in general universities.

At the swearing-in ceremony of Dr. Hilbert, the principal presided over: "I solemnly ask you to answer whether the oath can make you undertake the following commitments and guarantees with sincere conscience: you will bravely defend real science, develop it and add color to it; Neither driven by wealth nor fame, but only by the glory of God's truth. " I really want to know if there are any similar words at the doctor awarding ceremony in Tsinghua.

When Hilbert was old, he once heard a group of young people talking about a mathematician he knew. At that time, many famous people in Minkowski had died. He is especially concerned about the people being talked about. When everyone finished talking about how many children the man had, he asked, "... does he still exist ..."

Once in Hilbert's discussion class, a young man reported using a beautiful theorem. Hilbert said, "This is really a wonderful theorem. Who found it? " The young man stood blankly for a long time and said to Hilbert, "It's you ..."

Goettingen's widely circulated story about Minkowski said that he was walking in the street and found a young man silently thinking about a very important question, so Minkowski patted him on the shoulder and told him that "convergence is certain", and the young man smiled gratefully.

1909- 1934 The Department of Mathematics is Edmund Landau. Landau's work habits are very strange. Six hours of work and six hours of rest alternate. He received countless letters about proving Fermat's last theorem, but later he really didn't have the energy to deal with it, so he printed a batch of cards, which looked like this.

-

Dear _ _ _

Thank you for proving Fermat's last theorem.

The first error is on line _ _ on page _ _.

This invalidates the evidence.

E. Mr. Landau

-

Although many manuscripts have been returned, it is said that the rest are still more than 3 meters high.

The most incomprehensible thing about the universe is that it can be understood.

-Albert Einstein

When Einstein conceived the general theory of relativity, although his mathematician friends taught him a lot of Riemannian geometry, his mathematics was still not satisfactory. Later, he went to G? ttingen once and gave several lectures to many mathematicians such as Hilbert. Shortly after he left, Hilbert worked out the famous field equation, and Hilbert's mathematics was certainly much better than Einstein's. Soon, Einstein also came out. It is suggested that Hilbert consider the author of this thing. Hilbert said frankly: "Every child on Gottingen Road knows more about four-dimensional geometry than Einstein, but despite this, Einstein, not a mathematician, invented the theory of relativity."

The first spherically symmetric solution of Einstein's field equation, that is, Schwarzschild's solution, was given by the same person in the trench of World War I. Schwarzschild was a professor of astronomy in G? ttingen.

Edeton is a great astrophysicist. The following story is about how he boasted. Shortly after the publication of Albert Einstein's general theory of relativity, a reporter went to interview Eddington and said that only three people in the world understood this profound theory. I wonder who these three people are. Eddington bowed his head in thought and did not answer for a long time. The reporter couldn't help asking again, and Eddington said, "I wonder who the third person is ..."

Einstein described the general theory of relativity with mathematics, that is, geometry in curved space, and Italian mathematician Levi-Civita made outstanding contributions to this geometry. So, someone asked Einstein what he liked best about Italy, and he replied that it was fine Italian noodles and Levi-Civita.

Einstein, a student of Minkowski, missed countless classes. As for many years later, when Minkowski learned about Einstein's theory, he sighed, "Oh, Einstein never came to class-I really didn't expect him to do such a thing."

A. Coble was an American academician in the last century. He is very influential in algebra and geometry. It is said that he has numerous doctoral thesis topics: you prove a two-dimensional situation, he asks the next doctoral student to prove a three-dimensional situation, and then asks the next doctoral student to do a four-dimensional one. Later, a doctor named Gerald Huff not only did the five-dimensional situation, but also solved the general n, which made Coble's infinite doctors idle in the future. Coble was very angry.

Archimedes is more imaginative than Homer.

-Voltaire

After Einstein, it should be reasonable for john von neumann, a mathematician who made computers, to continue. Every time we use computer games, we should express our highest respect to Neumann.

Von Neumann once met a man who asked him a question that is familiar to all primary school students in China, that is, two people walked towards each other, and there was a dog running around in the middle, asking how many dogs they had left after they met. Find out the time of meeting first, and then take the speed of the dog. If I remember correctly, I heard that Mr. Su was on a bus in Germany when I was a child, and someone asked him this question. Of course, his old man's house won't feel any difficulty. Von Neumann also gave the answer in an instant. The questioner was disappointed and said that you must have heard of this trick. He refers to the above practice. Von Neumann said, "What's the trick? What I do is to work out every time the dog runs, and then work out the infinite series ... "

When Barnah (a talented mathematician in Poland) attended a math party in 1927, he poured vodka for Neumann with many mathematicians. In the end, Neumann was too drunk to go to the toilet, probably vomiting. But Bananchi recalled that when he came back to continue discussing mathematics, he didn't interrupt his thinking at all.

Mathematicians are born, not made.

-poincare

Math is harmful to health, so it's better not to read after the holiday.

The following is the length of existence of the most talented mathematicians in history on this timeline:

Pascal is 39 years old; Ramanujan 3 1 year; Abel is 27 years old; Galois 2 1 year; Riemann is 39 years old. Health is very important. De Moivre taught mathematics for a living when he was 2 1 years old. He was convinced that he was completely proficient in this subject. By chance, he was a guest at a duke's house, and Newton just sent his principles. He flipped through it and was surprised to find that mathematics is such a profound and beautiful subject. In this way, he bought the book, even if he had to run around for teaching, he had to tear off the pages so that he could carry them in his pocket and do research in his spare time.

Let's talk about the careers of several mathematicians as teachers. Most celebrities are not very good at giving lectures, or occasionally fail. For example, Newton once spoke to an empty lecture hall at the beginning. First, he is not very clear, and second, he is too difficult, so no one in Cambridge likes his class.

Let's start with some people you don't know.

Mondbrot is famous for drawing fractals. In fact, his uncle Mandelbrojt was a better mathematician and one of the earliest members of bourbaki. As a student, he came to France from Poland to study mathematics. After he went, he was seriously hurt mentally because he took Goursat's analysis class. However, Goursat always tells an old story that existed twenty or thirty years ago in a tone. After listening to the class for about three weeks, Mandelbrojt felt too far away from his dream class and even cried. However, a few years later, Bernstein came to Paris to comfort Mandel Breu, saying that Gulsat had taught him this way more than 20 years ago. But Goursat is very enthusiastic about people.

Imagine how naive Mandelbrojt is about knowledge. That kind of thing doesn't seem to belong to our time anymore.

Lin Deman, who proved the transcendence of π, is said to be one of the worst lecturers in history. Here are two stories about him, one is about his lecture, and the other is about the little things he studied in Paris, which is quite cute.

Legend has it that Lin Deman couldn't hear clearly most of the time, and he couldn't understand what he heard clearly. In a few cases, what he said is clear and easy to understand and wrong.

When Lin Deman went to Paris to study, he listened to Bertrand and Jordan. There were too few people studying mathematics at that time. Although Jordan is the leading mathematician in France, only three people attend his class, sometimes up to four, but one of them is because the classroom is warm.

Some mathematicians wrote it down below-

All mathematicians live in two different worlds. One is a crystal clear world composed of perfect ideal forms, an ice palace. But they still live in the ordinary world, and things are fleeting or vague because of their development. Mathematicians shuttle between these two worlds. In the transparent world, they are adults, but in the real world, they become babies.

-S. capel

1 1 I started to learn Euclid's books at the age of, and asked my brother to be my teacher. This is a great event in my life, as charming as first love.

There is a path across the field leading to the new south gate. I often go there alone to watch the sunset and think of suicide. However, I didn't commit suicide in the end, because I wanted to know more about mathematics.

-Bertrand Russell

I don't know what the world thinks of me; But in my own opinion, I seem to be just a child playing by the sea, and I am glad to find smoother stones or more beautiful shells from time to time. What is displayed in front of me is a sea of truth that has never been explored at all.

-Isaac Newton

In an interview, Thom, as a mathematician, discussed with two paleoanthropologists. When talking about why ancient people made a fire, an anthropologist said, because it can keep warm and keep out the cold; Another anthropologist said, because keeping fire can cook delicious meat. And Tom said, because when night comes, the fire is charming and colorful, which is the most beautiful.

Beauty is the eternal pursuit of our mathematicians and heroes.